Re: Kinematics - a vs. t graphs

[Bernard Cleyet <anngeorg@PACBELL.NET>]

L., have you tried asking John G?    If I had the time I'd try looking
at the piezo plate with an o'scope.   I suspect the only limit* on the
analog side is the pulse shape (rise time), also the min. range limit is
due to the pulse width.   With a very fast RT, the limit is the
bandwidth of the following amp. and the resolution of the ADC, for the
digital "side".

* this, as others have pointed out, assumes no spurious reflections,
flat, correctly oriented plate, etc.

".. not without some nontrivial
regularization assumptions."

Huh?    Resolution only need exceed the acceleration limited by the force and mass to the degree of accuracy desired.

the page below describes a novel way of increasing the accuracy limited by the frequency of the wave train.

http://216.239.33.104/search?q=cache:_hZoOHgFPnEJ:miyaweba.elec.ryukoku.ac.jp/miyashita/papers/jjap98y.pdf+acoustic+range+finder+vernier&hl=en&ie=UTF-8
<http://216.239.33.104/search?q=cache:_hZoOHgFPnEJ:miyaweba.elec.ryukoku.ac.jp/miyashita/papers/jjap98y.pdf+acoustic+range+finder+vernier&hl=en&ie=UTF-8>

bc, who must be missing something




Ludwik Kowalski wrote:

> We will start using the motion detectors next week.  Then
>  I will investigate the "noise."  As I remember, the plot is
> a practically noiseless horizontal line when the detector
> faces a wall.
>
> Now suppose the "wall" starts moving slowly toward me.
> I suspect that the display will be a stepwise function of x
> versus t. The ADC (analog-to-digital convertor) has only
> 7 bits (?) and this is likely to produce steps. The 9-bits
> ADC should display 4 times smaller steps. Ideally the ADC
> error should be much smaller than fluctuations on the
> analog side. Does anybody know how accurate are
> distance measurements on the analog side? What can
> be done to reduce them?
> Ludwik Kowalski
>
> On Wednesday, September 17, Gary Hemminger wrote:
>
>
>
> > "You cannot reliably infer the acceleration from samples
> > of the x and t coordinates, not without some nontrivial
> > regularization assumptions."
> >
> > We are using old Vernier software and motion detectors for Workshop
> > Physics labs in which we generate d, v, and  a vs. t graphs. The a vs t
> > graphs are always noisy, and generally look like the edge of a
> > carpenter's saw.  I'm not familiar with the latest software and
> > equipment, and wonder if cleaner graphs are now possible.
> >
> > Despite the difficulties mentioned in the thread above, I expect that
> > the main issue here is coming from the propagation of error.  If the
> > motion detector takes say 30 readings per second, then I assume that it
> > calculates 30 average velocities per second, and uses Ludwik's method
> > to find 30 average accelerations per second.  I find that the noise
> > varies
> > from one machine to another in my room despite similar setups and
> > conditions.